Raman spectrum (in aqueous solution) and force constants of MoO3S2−

Spectrochimica Acta, Vol. 34A, pp. 561 to 562. 0 Pergamon Press Ltd., 1978. Printed in Great Britain

Research Note

RAMAN

SPECTRUM (IN AQUEOUS SOLUTION) FORCE CONSTANTS OF MoO$ -

AND

(Received 10 January 1977) Abstract-The Raman spectrum of K2M00sS in aqueous solution was measured. This allowed a unique assignment of the fundamentals of the MOO@ ion. A plausible set of force constants was computed using the first order uerturbation theorv in conjunction with the exact force constants for MOO:and MoS:-.

INTRODUCTION

Thedifficulties associated with the preparation of complexes with pure monothiomolybdate using the method reported in literature [l] are well known [2]. As a consequence of this, up to now practically no physical property of Mo03S2is known. As we could now prepare pure KzMo03S, we have measured the Raman spectrum in aqueous solution which allowed a unique assignment of the fundamentals of MoO$(point group symmetry C,,). The results are presented in this communication. EXPERIMENTAL

KzMoOBS could be obtained according to a new method rkported by us [31. The Raman spectrum in aqueous solu-

tion (stabilized by addition of KOH) was measured using a Coderg laser Raman spectrometer equipped with a Kr-laser (excitation line 6471 A). The spectrum is illustrated in Fig. 1. The frequencies reported in Table 1 are accurate to & 2 cm- I. NORMAL COORDINATE

ANALYSIS

Based on the assignment reported in Table 1, a normal coordinate analysis was carried out for Mo03S2-. The exact force constants for MOO:- and MoS:- (from solution data) determined using the 92Mo/““‘Mo isotope shifts [4] were used as a first approximation. The initial symmetry force constants for MoOJS2- weredetermined from those of MOO:- and MoS:- directly by a method described by MATTES and BECHER [5]. In this connection, the value of MOO, S’-

I I

V,

cm -I

Fig. 1. Table 1. Vibrational fundamentals and assignment for MoOsS’Raman spectrum in aqueous solution* [cm-l] 900 (s) 846 (w) 472 (m)

Depolarization ratio

Assignment

0.1(O) 0.7(4) 0.2(6)

318 (m)

0.7(5)

237 (w)

0.7(4)

(C,,) from the

v,(Mo-0) v,(Mo-0) , v(Mo-S) &@--MO-O) 8,(0-Mo-0) p(MoO3)

* For frequencies of solid Na2Mo03S (not pure), see [8]. 561

(A,) (E) (AI) (A,) (E) (E)

RESEARCHNOTE

562

Table 2. Symmetry

force constants

Symmetry force constant Initial sea Final set 5

for MoOsS’-

(Cs,)*t

Calculated values of the frequencies in cm - 1 Final set4 Initial seq

Al

F11 F12 F1s F22

F23 Fs3 E F44 F45

F46 F55 F56

F66

3.12 0.74 0.07 7.01 -0.04 1.04

3.05 0.75 - 0.05 7.30 - 0.03 1.19

882

900

483

472

293

318

5.28 0.06 - 0.06 1.02 - 0.02 1.02

5.43 0.07 - 0.08 1.03 -0.01 0.96

834

846

316

318

245

237

AcknoM,ledyements-We thank the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen lndustrie and NATO (Scientific Affairs Division) for their financial support. One of the authors (C.T.) thanks also the DAAD (Germany) for the award of a fellowship.

*The force constants are based on the symmetry coordinates of ALDUS and MILLS [9], where S, is v(Mo-S), S2 is v,(Mo-0), Ss is S,, Se is v,(Mo-0), Ss is 6, and s6 is p. t Fii, Fi2, FU and F.u are in mdyn/A; Fis, F23, F45 and Fe6 in mdyn; Fss, F55r F5s and Fs6 are in mdyn/A. 1 Obtained by transferring the exact force constants for MOO:- and MoS:[4]. (i Based on equation (1) and the initial set (see text). fs(Mo-S) was transferred from MoSzand those of ~(Mo-0) and f,,(Mo-O/Ma-0) were transferred from MoOa-. For the other constants, the average of the values Since in MC& and MoS:- were used in the calculations. the exact geometrical parameters for MoOsS’are not known, we used d(Mo-S) = 2.18A and d(Mo-0) = 1.77 A which are the experimental values corresponding to K2Mo04 and Cs2MoOSs [6]. Both @-MO-O) and b(S-Mo-0) were assumed to be tetrahedral. As seen from Table 2, the initial force field based on the above deliberations. renroduces the frequencies of Mo0sS2rather well. In order- to improve the fit with the experimental data on the frequencies, the first order perturbation approach [7] was utilized in refining the initial set of force constants. Thus, the final set of force constants was computed using the relation F fina,= (-h ‘)‘&

L

1

where Lo is the eigenvector matrix corresponding to the initial force field and Aexp is a diagonal matrix containing the squares of the measured frequencies (this method is applicable if the initial set of force constants is close to the exact one). The results are given in Table 2. The computed values of f,(Mo-0) and-f,(Mo-S) (6.05 mdyn/A and 3.05 mdyn/A respectively) indicate that while the M&O bond is stronger than in MOO:(5 = 5.86) the reverse is the case for the MO-S bond (fa = 3.12) (compared to that in MoS:-) (see Table 2 and [4]).

(1)

A. MILLER N. MOHAN H. D~RNFELD C. TELLEZ

Faculty of Chemistry University ofBielefeld 4800 Bielefeld u! Germany

REFERENCES I-11 - _ G. KR&s, Liebigs Ann. Chem. 225,6 (1884). The preparation method given in [l] cannot be repeated. PI DR. C. H. MITCHELL, University of Reading, England (private communication); DR. D. KRONETK, Konstanz, Germany (private communication). [3] A. MUELLERand H. DORNFELD, 2. Awry. Al/g. Chem. (to be published). [4] A. MUELLER,N. WEINSTOCK, N. MOHAN, C. W. SCHL~PFERand K. NAKAMOTO, Appl. Spectroscopy 21, 257 (1973); A. MILLER, F. K~NIGERand N. WEINSTOCK, Spectrochim. Acta 30A, 641 (1974). [5] R. MATTESand H. J. BECHER,Z. Phys. Chem. (Frankfurt) 61, 177 (1968). [6] A. MUELLERand E. DIEMANN, MTP International Review of Sciences. Series Two, Vol. 5, v. 71. Butterworth. London (1974). [7] E. B. WILSON,J. C. DECIUSand P. C. CROSS,Molecular Vibrations, p. 188. McGraw-Hill, New York (1955). [S] M. J. F. LEROY, M. BURGARD and A. MILLER, Bull. Sot. Chim. France 4, 1183 (1971). [9] J. ALDOUSand I. M. MILLS, Spectrochim. Acta 18, 1073 (1962).